VOLUMES?, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 29 SEPTEMBER 1986

Comment on **Local Structure at Mn Sites in Icosahedral Mn-Al Quasicrystals"

In a recent Letter, Stern, Ma, and Bouldin (SMB)^ report extended x-ray-absorption fine-structure (EX-AFS) results for icosahedral Al^Mn. SMB claim that their EXAFS data support a model involving two Mn sites, one of which is like that in oAl^Mn. These sites occur in the ratio 1:T, with r = (1 -f V5)/2. They claim that the icosahedral phase is structurally unrelated to the a-AlMnSi^'^ phase which has been proposed as a prototype. In this Comment, I raise questions about the data analysis which leads to the above conclusions.

The data themselves are assumed correct; only the analysis is being criticized here. The most important point is that EXAFS cannot distinguish the presence of different sites. EXAFS delivers only information on distance distributions,"^ except in some special cases. The a phase of Al-Mn-Si has two Mn sites, whose dis­tance distributions overlap. Thus, EXAFS cannot separate the two crystallographically inequivalent sites in the a phase. SMB argue that the a phase cannot be a correct model for the icosahedral phase because it has sites occupied in a 1:1 ratio, instead of 1:T, but the sites they refer to are crystallographic sites, not peaks in an effective radial distribution function.

Even if the EXAFS is uniquely decomposable into two contributions, the identification with different Mn sites is not assured. Has the EXAFS been decom­posed uniquely into two contributions? One piece of evidence for this decomposition is the slope change in the plot of the logarithm of the ratio of amplitudes. While such a slope change can result from a bimodal distribution of distances, it also results from any distri­bution having a negative fourth cumulant. The decomposition was done on the assumption that one contribution was that of the crystal, but with adjustable coordination number, distance, and second and third moments. The leftover signal was considered to be the other contribution. The fitted radial distribution comes out as a sharp peak (first component) sitting on a broad peak (second). The sharp component was subtracted from the whole spectrum, and its parame­ters adjusted until the Fourier magnitude of the remainder was minimized. If the amount subtracted were only enough to obliterate the sharp component, then the broad one would contribute some Fourier magnitude. By subtracting slightly more "sharp peak," we remove the leftover amplitude. Thus, this subtraction method overestimates the coordination number associated with the sharp component and dis­torts the broad one. This method is internally incon­sistent, since the broad component is required to have

very small amplitude in a certain distance region, yet is not constructed from functions for which this is possi­ble.

A paragraph is devoted to two small peaks in the Fourier transform, at 5.8 and 7.0 A, which are present in the crystal and not in the quasicrystal. Arguments are put forward as to why these peaks are expected in the crystal. A simulation of the EXAFS spectrum of o-Al^Mn shows only one peak, at 6.1 A. That the peaks in SMB's Fourier magnitude come at the wrong places, and one is not there at all in the simulation, strongly suggest that they are noise peaks.

It is stated that Mossbauer measurements show the presence of two sites, also in the ratio 1:T. Recent Mossbauer results^ show that the spectrum is better fitted with either a continuous distribution of quadru-pole splittings, or a discrete one with more than two Mn sites, than by one with two Mn sites. The Moss­bauer results cannot be used as evidence for the ex­istence of exactly two Mn sites.

SMB ask why the quasicrystal phase is rare, and claim that it is only seen in systems structurally related to oAl^Mn. Since Ref. 1 was written, systems in which the o-Al^Mn structure does not occur, such as Al-Mg-Zn,^'^ have been made icosahedral. Part of their discussion involves the short Mn—Al bond (2.435 A ) in oAl^Mn, which they claim is absent in the icosahedral phase. This absence has not been demonstrated, nor have limits to the abundance of short bonds been set.

I conclude that the SMB result of two sites, in 1:T ratio, with identical distances and different disorders, is not supported by the given analysis.

Matthew A. Marcus Bell Laboratories Murray Hill, New Jersey 07974

Received 16 December 1985 PACS numbers: 61.50.Em, 61.10.Lx, 61.55.Hg, 64.60.My

IE. A. Stern, Y. Ma, and C. E. Bouldin, Phys. Rev. Lett. 55, 2172 (1985).

2V. Elser and C. H. Henley, Phys. Rev. Lett. 55, 2883 (1985).

^M. Cooper and K. Robinson, Acta Crystallogr. 20, 614 (1966).

'̂ P. A. Lee, P. H. Citrin, P. Eisenberger, and B. M. Kin-caid. Rev. Mod. Phys. 53, 769 (1981).

^M. Eibschutz, H. S. Chen, and J. J. Hauser, Phys. Rev. Lett. 56, 169 (1985).

^P. Ramchandrarao and G. V. S. Sastry, Pramana 25, L225 (1985).

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